Investigating the domain of validity of the Gubser solution to the Boltzmann equation

Abstract

We study the evolution of the one particle distribution function that solves exactly the relativistic Boltzmann equation within the relaxation time approximation for a conformal system undergoing simultaneously azimuthally symmetric transverse and boost-invariant longitudinal expansion. We show, for arbitrary values of the shear viscosity to entropy density ratio, that the distribution function can become negative in certain kinematic regions of the available phase space depending on the boundary conditions. For thermal equilibrium initial conditions, we determine numerically the physical boundary in phase space where the distribution function is always positive definite. The requirement of positivity of this particular exact solution restricts its domain of validity, and it imposes physical constraints on its applicability.

17 pages, 6 figures. v2: Minor corrections in the text. Updated references. Published version

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• Anisotropic hydrodynamics for conformal Gubser flow
• Exact solutions of the Boltzmann equation and optimized hydrodynamic approaches for relativistic heavy-ion collisions
• Dissipative type theories for Bjorken and Gubser flows
• Maximally Symmetric Boost-Invariant Solutions of the Boltzmann Equation in Foliated Geometries